A quantum moat barrier, realized with a finite square well

The notion of a double well potential typically involves two regions of space separated by a repulsive potential barrier. The solution is a wave function that is suppressed in the barrier region and localized in the two surrounding regions. Remarkably, we illustrate that similar solutions can be achieved using an attractive "barrier" potential (a "quantum moat") instead of a repulsive one (a "quantum wall"). The reason this works is intimately connected to the concepts of "orthogonalized plane waves" and the pseudopotential method, both originally used to understand electronic band structures in solids. While the main goal of this work is to use a simple model to demonstrate the barrier-like attribute of a quantum moat, we also show how the pseudopotential method is used to greatly improve the efficiency of constructing wave functions for this system using matrix diagonalization.